In the current work, an incompressible thermal flow in a micro-Couette in the presence of a pressure gradient is investigated utilizing the analytical solution of the Burnett equations with first-order and second-order slip boundary conditions, for the first time. The lower plate of this micro-Couette is stationary while the upper plate moves with a constant velocity. Both non-dimensional axial velocity and temperature profiles were obtained using two types of the slip boundary conditions and compared in transition flow regime (0.1≤ Kn ≤10). The results show that the effect of the rarefaction is considerable on both velocity and temperature profiles in this regime. Because of the presence of pressure gradient in direction of the flow, both the non-dimensional velocity and temperature profiles are obtained parabolically and become flatter as the Knudsen number increases. Besides, both Poiseuille number and Nusselt number were obtained using analytical solution. The obtained results show that the Poiseuille number and Nusselt number decrease with increasing the Knudsen number. It should be noted that at the absence of an axial pressure gradient, velocity profile is obtained linearly and show a good agreement with the other works in literature.